I'd say it's pronounced a little closer to /nyook mom/, but the y is barely present.

Nuoc mam is the Vietnamese name for the sauce. The Thai version of fish sauce tastes slightly different; but the Thai version is probably the best kind you can find in the store.

Nuoc mam seems to be made one of 2 ways:

A barrel is filled with layers of salt and fish. This is then left for months out on the beach (the fish are caught and put straight into the barrels). I think it's something like 9 months. At the end of this period they open a spigot on the bottom of the barrel and drain out the fluid. This is the "first press" or "extra virgin" fish sauce that you'd want to use on your table. Some fluid is then poured back onto the top and more stuff is done to get more fish sauce out, but it's a lower grade that you'd use in cooking things that need a little flavor, not the sauce you put right on the table.

Anchovies are ground into a paste to make mam, which is then allowed to ferment and the fluid is extracted. Mam means, roughly, "fish paste" and most vietnamese recipes that now use nuoc mam used to use mam. Nuoc means roughly "water from", so nuoc mam is "water from fish paste".

Nuoc mam has a delightful salty, smoky, fishy taste. A simple bowl of rice is turned into an exciting meal with some nuoc mam poured over it. It smells nothing at all like butt. But it does have the basic issue that it's a fermented food and fermented foods are almost always gross to foreigners. (Imagine what most asians think of fermenting milk and eating the hardened result that we call cheese)

In Vietnamese food, nuoc mam is used everywhere, much like soy sauce is used everywhere in Chinese or Japanese food. (Except on the new and full moons for a lot of vietnamese, when they go vegetarian)

"Nuoc" simply means water. There are many kinds of "mam" - which is anything salted and fermented.

Nuoc mam is most often served on the table in a diluted form. Garlic, sugar, chilies, carrots, lime or lemon juice are commonly added. The resultant condiment is something that tickles many parts of your palate. You have something salty/sweet/sour/ and spicy hot as well as fishy. Exactly how this is done varies greatly from region to region in Vietnam.

#1 is the correct way to make nuoc mam. The leftover anchovies can be used as mam after the extraction.